[UPSC IFoS 2023] Special Theory of Relativity (Q327, 10M)

In a reference frame S, an event 1 occurs at the origin at t = 0 and another event 2 occurs at x = 4000\text{ m} and time t = 5 \times 10^{-6}\text{ s}. Find the time interval between the events as registered by clock in a frame S' moving with speed v = 0 \cdot 6 \, c relative to S along the common X-X' axis, the origin coinciding at t = t' = 0\,.